1. Field of the Invention
This invention relates to an inverse control system, which is used in cascade connection to a linear system having one or more input points and one or more output points, with the impulse responses of signal transmission channels between any such input and output points being substantially finite (the linear system being hereinafter referred to as linear FIR (finite impulse response) system), for realizing an inverse control of the linear FIR system such as to make its impulse response, or signal transmission characteristics (i.e., frequency versus amplitude characteristics and frequency versus phase characteristics) of the linear FIR system to be desired impulse responses (signal transmission characteristics).
The inverse control system of a linear FIR system can be applied to various fields. For example, it can be applied to a loudspeaker-system. In this case, inverse control of input-signals to the loudspeaker-system can be utilized for realizing a desired sound pressure distribution at one or more microphones or at a person's ears in a sound field in an ordinary room. Also, it can be utilized for suppressing the howling phenomenon by removing the acoustical coupling between loudspeakers and microphones. Further application is the active noise control for suppressing room noise at desired points in a room.
The inverse control system can also be applied to a microphone-system. In this case, inverse control of output-signals of the microphone-system can be utilized for dereverberation of acoustic signals which radiate in a room, and for suppressing undesired acoustic signals (i.e. room noise etc.) which pollute a desired acoustic signal.
Further, where the linear FIR system is an electromagnetic wave propagation system, inverse control can be utilized for processing an input signal supplied to transmitting antennas to obtain distortionless transmission such that a distortionless signal can be received at a receiving point in the electromagnetic wave propagation system. Inverse control can also be utilized for processing intercepted signals by receiving antennas to remove multi-path, ghost and noise signals.
2. Prior Art
FIG. 1 shows a prior art method for controlling the sound pressure at a single point for the sake of the brevity. A method for control of two or more points is based on entirely the same principle. It is assumed that the sound pressure from a virtual loudspeaker S' that is received by a microphone 11, which is disposed in a sound field 40 where there are reverberations, can be reproduced without using the virtual loudspeaker S' by using a loudspeaker 1.sub.1 disposed at a different position. If this can be done, the result is the same as if an acoustic signal were being radiated from the virtual loudspeaker S' in spite of the fact that the acoustic signal is actually being radiated from the loudspeaker 1.sub.1. To produce this situation, coefficients of a filter 21.sub.1 through which a signal is supplied to the loudspeaker 1.sub.1, may be suitably set such that the impulse response of a channel between the loudspeaker 1.sub.1 and microphone 11.sub.1 is equal to that of a channel between the virtual loudspeaker S' and microphone 11.sub.1. That is, the signal may be inversely controlled through the filter 21.sub.1.
In FIG. 1, the sound field 40 in the room can be regarded as a linear FIR system, with the loudspeaker 1.sub.1 acting at an input point of the system as a transmitting element for supplying a signal to the system and the microphone 11.sub.1 acting at an output point of the system as a receiving element.
Usually, therefore, an arrangement as shown in FIG. 2 is set up. A transmitting element 4.sub.1 is disposed at an input point 3.sub.1 of a single-input single-output linear FIR system. A signal from the transmitting element 4.sub.1 is fed to the linear FIR system 2.sub.1. A signal from a signal source 13 is fed through a filter 21.sub.1 to the transmitting element 4.sub.1. An output signal which has characteristic corresponding to a desired impulse response, is obtained from an output point 5.sub.1 of the linear FIR system 2.sub.1.
To simplify the description, inverse control of the linear FIR system 2.sub.1 will be considered, in which an input signal x(k) (K=1, 2, . . . ) from the signal source 13 and the output signal y(k) of the linear FIR system 2.sub.1 are made equal on the premise that there would be no delay (i.e., delay time of the impulse response) in the linear system 2.sub.1. In FIG. 2, the relationship between the input signal and the output signal y(k) is given by the following expression (1a) EQU y(k)=h.sub.1 (k) .circle.* g.sub.11 (k) .circle.* x(k) (1a)
wherein h.sub.1 (k) denotes coefficients of the filter 21.sub.1 and g.sub.11 (k) is an impulse response represented by W.sub.11 discrete signals of the linear FIR system 2.sub.1. Since the output signal y(k) is intended to be made equal to the input signal x(k), the following expression (1b) must be satisfied. EQU .delta.(k)=h.sub.1 (k) .circle.* g.sub.11 (k) (1b)
where ##EQU3## The intended inverse control can be realized by obtaining coefficients h.sub.1 (k) of the filter 21.sub.1 which satisfy expression (1b). However, in the case where the impulse response g.sub.11 (k) of the linear FIR system 2.sub.1 has a nonminimum phase (e.g., such as a system where there are a reflected waves), that is, where the zero of the z-transform, g.sub.11 (z), of the impulse response g.sub.11 (k) is also found outside a unit circle on the z-plane, the filter 21.sub.1 which satisfies ##EQU4## where h.sub.1 (z) is the z-transform of the filter coefficients h.sub.1 (k), is unstable. Therefore, the inverse control noted above can not be realized. This is disclosed in S. T. Neely and J. B. Allen, "Invertibility of a Room Impulse Response", J. Acoust. Soc. Am., 66(1), pp. 163-169, July, 1979.
In the prior art, therefore, the filter 21.sub.1 has been realized as a stable and simple FIR filter, which has coefficients h.sub.1 (k) which minimize the cost function given as ##EQU5##
Inverse control of a multiple-input multiple-output linear FIR system has been performed in a similar manner.
Such prior art technology, however, has theoretical problems as follows: The filter coefficients h.sub.1 (k) obtained in the prior art minimize the square error ##STR1## but usually do not make it zero. Therefore, it is impossible to realize exact inverse control.
The magnitude of ##STR2## and characteristics (i.e., frequency versus amplitude characteristic and frequency versus phase characteristic) of e(k) depend on the impulse response g.sub.11 (k). Therefore, the performance of the inverse control attainable in the prior art varies greatly with the linear FIR system that is controlled.
Further, it is shown in the literature noted above to connect, for an inverse control, a filter to the output side of a microphone, which is adapted to receive sound from an acoustic signal source (i.e. a loudspeaker, a person's mouth etc.) provided in a sound field of a room, for the purpose of removing reverberations or echoes caused by wall reflections. FIG. 3 shows a set-up for inverse control of a single-input single-output linear FIR system similar to the above case. A transmitting element 4.sub.1 is disposed at an input point 3.sub.1, and its signal is fed to a linear FIR system 2.sub.1. The output signal of the linear FIR system 2.sub.1 is received by a receiving element 6.sub.1 disposed at an output point 5.sub.1 of the system 2.sub.1. The output signal of the receiving element 6.sub.1 is fed to a filter 21.sub.1 to obtain a signal with desired characteristics. The output signal y(k) in FIG. 3 is expressed as EQU y(k)=g.sub.11 (k) .circle.* h.sub.1 (k) .circle.* x(k)
In this case, if the inverse control is to make the output signal y(k) of the filter 21.sub.1 equal to the input signal x(k), the following relationship must be satisfied EQU .delta.(k)=h.sub.1 (k) .circle.* g.sub.11 (k)=g.sub.11 (k) .circle.* h.sub.1 (k)
where ##EQU6## These expressions are identical with the equations (1a) and (1b), so that it is necessary to obtain filter coefficients h.sub.1 (k) which satisfy these equations. In the prior art, however, the filter coefficients h.sub.1 (k) have been obtained in a manner similar to that mentioned previously so that the cost function (2) may become minimum. Further, the same procedure mentioned above has been employed for an inverse control of the output of a multiple-input multiple-output linear FIR system. Therefore, the same problems are posed in the inverse control of the output signal of a linear FIR system as those in the case of the inverse control of the output signal of a linear FIR system.